Population genetics models play a crucial role in many aspects of modern disease gene mapping studies, from identification of population stratification to haplotype phasing. Though these studies to date have largely been per- formed in populations of European descent, in the coming years they will expand to a large number of diverse populations. This proposal outlines novel statistical models for describing allele frequencies in multiple populations, with applications relevant to the next generation of disease mapping studies. First, I describe a novel model for inferring population history from genome-wide allele frequency data. The history of a population is an important determinant of the amount of genetic variation and extent of linkage disequilibrium in the population, but current methods for inferring history are either limited to a small number of populations or do not allow for gene flow be- tween populations. A proposed approach overcomes these problems, and will allow for efficient modeling of allele frequencies in a large number of diverse populations. Second, I describe an approach for local ancestry inference in populations with arbitrarily complex admixture histories. Many populations involved in disease mapping studies are the result of mixtures between multiple populations (e.g. Latinos throughout the Americas) or between populations without close modern equivalents (e.g. many populations in India). Though local ancestry inference in these populations is important for localizing association signals, most current methods are not designed for these situations. I propose a model that explicitly accounts for the relationship of ancestral populations to modern ones, and will allow for efficient local ancestry inference in populations with complex demographic histories. Finally, I describe a method for detecting subtle changes in allele frequency due to natural selection. It is likely that natural selection in humans acts to cause small shifts in allele frequency at many loci; however, most methods to detect selection rely on rapid fixation of strongly selected alleles. I propose a method, based on explicitly modeling the demographic relationship between populations, to overcome this obstacle. PUBLIC HEALTH RELEVANCE: Population genetics models are crucial for many aspects of disease gene mapping studies. This proposal de- scribes novel models for describing ancestry in diverse human populations, particularly in admixed populations like African-Americans and Latinos in the United States. The technology developed will be applicable in disease gene mapping studies in diverse populations.